Many villains are ruthless and uncaring about the world around them, perfectly willing to hurt innocents to further their gains, but it's not always this way. Sometimes, you'll run across a villain who, while just as greedy and self-serving, still makes sure not to hurt those around him, and is not willing to kill and destroy innocent lives just to get ahead. Offer them infinite power if they'd just kill a single innocent, and expect them to say no; of course, that doesn't mean they won't accept the infinite power if they could get around the whole "killing the innocent" part. These villains are some of the more human villains out there.
Generally, this is shown as villains trying to avoid harming people who aren't involved, and making sure not to kill innocent people. Unfortunately for our heroes, they don't count, so they can expect every weapon at these villains' disposal to be aimed at them.
This is a must for the Hitman with a Heart an Anti-Villain, Noble Demon, or Anti-Hero, a form of Even Evil Has Standards, and is a Sub-Trope of sorts of Affably Evil. See also A Lighter Shade of Grey, when something like this makes them look good despite a total willingness to kill the guilty, and Punch-Clock Villain, for villains who take this to the next level, and only act villainous because it pays the bills (though it's not a given that they'll be like this). A Blood Knight may also exhibit this, although in their case it may be more down to innocents never putting up a good fight. Don't expect the Omnicidal Maniac and Psycho for Hire to adhere to this trope.
Some subtropes denote specific groups or classes of persons as off-limits:
Wouldn't Hurt a Child — kids, because Children Are Innocent.
Wouldn't Hit a Girl — women. Expect this villain/antihero to be a Wife-Basher Basher as well.
Would Not Shoot a Civilian — noncombatants.
Kick Them While They Are Down — the injured or incapacitated.
Would Not Shoot a Good Guy — those whose opposition is honest but misinformed.
Other common "off-limits" groups include medical personnel (contrast Shoot the Medic First) and clergy. Contrast Targeted to Hurt the Hero, where a villain deliberately targets an innocent to break The Hero.
May be a form of Villainous Vow. Pay Evil unto Evil is the kind of antagonism permitted to characters following this trope. The opposite of You Can't Make an Omelette.... This trope is generally ubiquitous in heroes so list villains and antiheroes here.